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Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial…

We propose a new way of thinking about deep neural networks, in which the linear and non-linear components of the network are naturally derived and justified in terms of principles in probability theory. In particular, the models…

Deep Learning using the eponymous deep neural networks (DNNs) has become an attractive approach towards various data-based problems of theoretical physics in the past decade. There has been a clear trend to deeper architectures containing…

Deep generative neural networks (DGNNs) have achieved realistic and high-quality data generation. In particular, the adversarial training scheme has been applied to many DGNNs and has exhibited powerful performance. Despite of recent…

In this paper, we develop and explore deep anomaly detection techniques based on the capsule network (CapsNet) for image data. Being able to encoding intrinsic spatial relationship between parts and a whole, CapsNet has been applied as both…

Convolutional neural networks use pooling and other downscaling operations to maintain translational invariance for detection of features, but in their architecture they do not explicitly maintain a representation of the locations of the…

We introduce a novel concept for spiking neural networks (SNNs) derived from the idea of "linear pieces" used to analyse the expressiveness and trainability of artificial neural networks (ANNs). We prove that the input domain of SNNs…

Deep neural networks with alternating convolutional, max-pooling and decimation layers are widely used in state of the art architectures for computer vision. Max-pooling purposefully discards precise spatial information in order to create…

Ensembling neural networks is an effective way to increase accuracy, and can often match the performance of individual larger models. This observation poses a natural question: given the choice between a deep ensemble and a single neural…

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…

Most uses of machine learning today involve training a model from scratch for a particular task, or sometimes starting with a model pretrained on a related task and then fine-tuning on a downstream task. Both approaches offer limited…

We propose a novel perspective to understand deep neural networks in an interpretable disentanglement form. For each semantic class, we extract a class-specific functional subnetwork from the original full model, with compressed structure…

Deep learning models frequently make incorrect predictions with high confidence when presented with test examples that are not well represented in their training dataset. We propose a novel and straightforward approach to estimate…

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

Several methods have been proposed to explain Deep Neural Network (DNN). However, to our knowledge, only classification networks have been studied to try to determine which input dimensions motivated the decision. Furthermore, as there is…

Modulation classification, an intermediate process between signal detection and demodulation in a physical layer, is now attracting more interest to the cognitive radio field, wherein the performance is powered by artificial intelligence…

One of the distinguishing characteristics of modern deep learning systems is that they typically employ neural network architectures that utilize enormous numbers of parameters, often in the millions and sometimes even in the billions.…

Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation…

Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…

Deep learning has excelled in image recognition tasks through neural networks inspired by the human brain. However, the necessity for large models to improve prediction accuracy introduces significant computational demands and extended…